The present invention relates to the real-time full scope simulation of the dynamic operation of a nuclear powered electrical generating plant for training plant operators.
The increasing demand for well-trained power plant operators together with the complexity of modern day power plants has led to the realization that the simulator is the most effective tool for such training.
Also, with advancements in nuclear power plant technology, experienced operators from time-to-time need retraining in order to be competent. An actual nuclear plant cannot provide the operator with the required experience, such as starting up, changing load, and shutting down, for example, except after years of experience; and even then, it is unlikely that he would observe the effect of important malfunctions and be able to take the best corrective procedures.
Although simulators have been used for many years, in power plant design, it is only recently that they have been used for power plant operator training.
An article in the July 22, 1968 issue of "Electrical World" entitled "Nuclear Training Center Using Digital Simulation" briefly describes the installation of a boiling water reactor plant simulator. An article in the same publication in the Oct. 6, 1969 issue entitled "Huge Simulator to Ready More Reactor Operators" discusses the proposed installation of a pressurized water reactor simulator. In Volume 10, No. 5 of the publication "Nuclear Safety" published during September and October, 1969 is an article entitled "Training Nuclear Power Plant Operators With Computerized Simulators"; and in the June, 1972 issue of the publication "Power Engineering" there is an article entitled "Simulators" which describes a number of power plant operator training simulators presently in use or proposed.
Design simulators usually cover only a small part of the process, and may run slower or faster than real-time; while training simulators must operate and respond in a manner identical to the actual plant. A design simulator may involve only a narrow range of conditions, while a training simulator must simulate from "cold" shutdown to well beyond normal operating conditions. A design simulator usually involves only the major process, while a training simulator should cover every auxiliary system with which the plant is concerned.
Training simulators presently in use for operator training, which are more or less complete in their simulation, utilize a digital computer connected to control consoles that are identical in operation and in appearance to the plant being simulated. Also, an instructor's console is connected to control the simulator, introduce malfunctions, initialize the selected plant at selected states of operation and perform other functions useful for training purposes. These computers have been of the same type used for aircraft training in some instances, and process control in others.
A full scope simulation of a nuclear power plant for operator training is of such extensive scope that it is advantageous to provide as many modeling simplifications as possible within the limits of steady state and transient accuracy. The mathematical modeling of a nuclear power plant is concerned with the materials, energy and volume balances, which often result in mathematical variables such as temperature, pressure, material flows and flow rates, concentration of materials, specific volumes and enthalpies, mechanical speeds, vibrations, electrical current, voltage and frequency, etc. A conference paper published by the Institute of Electrical and Electronic Engineers entitled "Mathematical Modeling for Power Plant Operator Simulators" written by B. H. Mutafelija et al, discusses many of the problems and desirable features connected with the mathematical modeling of power plant simulators.
The simulation of the power plant must be of sufficient detail and accuracy that the operator cannot distinguish between the behavior of the simulator and that of the actual plant under conditions of cold startup, hot restart, normal load changes, and numerous malfunctions causing a load cut-back or a complete shut-down.
In order to attain the accuracy required over a complete range of operation of a system that is non-linear, such as where it includes a plurality of heat exchangers in a feedwater system, and at the same time provide as many modeling simplifications as possible, it is desirable to calculate physical properties which provide for the greatest amount of accuracy, and simplification in calculation, and at the same time to utilize a curve fit that is accurate for the entire range of operation. Where there are a number of heat exchangers, such as feedwater heaters, in a feedwater system for example, it is desirable that for purposes of simulation they be lumped into as few equivalent feedwater heaters as possible.
For the single equivalent heaters, it is then desirable to use a dynamic energy balance equation for calculating a value dependent upon the dynamic behavior of outlet enthalpy. A value for condensed steam enthalpy can then be calculated with a curve fit of the outlet enthalpy, and finally a value for pressure can be effectively calculated using a curve fit function of condensed enthalpy.
In the dynamic simulation of the physical properties of steam and water in such a system, for example, where the numerical values of such properties are used in other simulations or continuously displayed or recorded through their entire operating range, such as the calculation of pressure in the feedwater heaters using a curve fit function of condensed enthalpy, it is necessary that such values be accurate and that the meters and recorders act in an identical manner to the system being simulated. To effect such a result, for physical values that are non-linear, that is, where the value of one physical property does not increase or decrease proportionately with the increase or decrease of another physical property, it is desirable to segment such values so that relatively simple calculations can be made with a minimum of error for each segment and provide continuity between segments. It is also desirable to effect such results with a minimum number of segments in order to minimize the complexity of the calculations and the amount of information required to be stored in the computer performing such calculations.
A spline fit function for the properties of steam and water at saturation, an extreme degree of accuracy is exhibited, provided that the number and location of the node points on the entire actual physical curve are such that the calculated spline curve equals or closely approximates the actual physical curve throughout its entire range. Thus, in finding the location and number of node points or intersections between segments, it is desirable that the minimum number of nodes be selected for a given allowable error. For such a given number of nodes, the actual position on the curves must be accurately determined so that the pointwise maximum error is minimal. In the past, several attempts have been made to optimize the node positions in cubic spline approximations. Various approaches have been used ranging from pure experimental node insertion on the curve, to algorithms based on the least square or on Chebyshev norms. The problem of finding optimum position of nodes for a given allowable maximum error leads to an excessive number of nodes if there is no prior knowledge about the curve to be approximated. Thus, in finding the best or optimum position of the nodes when their number is fixed, there have been several approaches. One approach is the minimization of a distance function; but the equations of such an approach have a very non-linear form, and are difficult to handle in a computer. Another approach is a search technique which will of course give the optimum node position after a long period of time, but at the same time may not be a completely convergent procedure.
In contrast, it is desirable to obtain optimum node position for a cubic spline curve fit by using the second derivative of the cubic spline which is a piecewise linear function. This permits a procedure that optimizes the area under a piecewise linear curve by solving a set of first order non-linear differential equations. The determined node positions are used to be the optimal positions of the nodes of the cubic spline itself. This method provides simplicity and rapid convergence for a wide variety of physical curves that possess a certain degree of smoothness, such as steam and water properties, for example.